Assign colour to vertices given face texture, and enable conversion to a point cloud
If you want to make each vertex store color from the appropriate place from the texture you want to bake texture to vertex colors. In case of baking in Blender this means you want your objects to be unwrapped and have a texture assigned to faces of the starting mesh.

First, unwrap the mesh if it hasn't been already. Then, if Cycles render engine is chosen, create a new scene / project and somehow transfer your mesh object there (Ctrl+C > Ctrl+V between different files can be handy, or append it from File > Append > Objects).   

In the new project choose Blender Internal as render engine  (see how). 

Then assign desired texture to faces of the mesh. To do so, open 2 editors in Blender window and choose one of them to be UV/Image editor (see more on this). In 3D viewport, enter Edit mode and select all. In the UV editor UV map should appear (see more info here if it doesn't). Choose your image texture you want to bake from in the UV editor via the dropdown list below the image.
Create a material for the object (default one works fine), then create new material texture for that material, its type by default should be Image or Movie. Choose image to bake to once more, this time in the dropdown list in the texture settings, Image rollout. Make sure Mapping is set to UV.



From this point you're left only to bake. In the Properties editor go to Render tab, scroll it to the Bake rollout and choose Textures. Below enable Bake To Vertex Colors option and press Bake button.



Note that quality of bake depends on density of geometry of the mesh.



Regarding the Bake UV textures to vertex colors addon. It makes it possible to bake in Cycles the same, but there's a small nuance - it expects texture to be assigned the same as in Blender Internal, i.e via UV editor to the face textures (however the addon doesn't require creating a material and assigning a texture to that).
Cycles doesn't do that since it doesn't use face textures to map images to mesh, so for baking with that addon in Cycles you'd need to switch to Internal, assign texture to faces with all selected in UV editor as explained above, then switch back to Cycles and bake.